Berlin sees two flights passing through every week from one different airlines, so you're bound to find one that works for you.
The cheapest airline to fly to with is normally Norwegian. Play around with the search options to see what you can find.
To find the best deal, why not look at other options in Germany? Some other cities may have cheaper options for flights and accommodation.
Norwegian Air Shuttle are the most popular airlines for flying to Berlin. Whoever you want to fly with, it's best to book your flights in advance, particularly if you want to fly on a specific date – otherwise they may sell out. Once you've booked, why not take a look at accommodation? Simply click on the ‘Hotel’ tab at the top of the page.